Data collected as part of “Decisions about chocolate are processed differently than decisions on gambles: Evidence from eye-tracking” by Betty E. Kim-Viechnicki.
A conjoint analysis was conducted to help understand how consumers make choices regarding chocolate purchases. Participants to a survey responded to questions such as the following:
Each trial had three alternatives to choose from consisting of a brand and type of a chocolate and the corresponding price. In addition to the type of chocolate, the number of times each respondent fixated over one of the attributes was recorded. Using this data we are able to answer the question of what attributes of chocolate to consumers consider most important in their purchsing decision.
Using the mlogit() function in R, we were able to implement a multinomial logistic model with our dataset. This model differs from a general logistic model in that it considers the choices of a respondent in each trial.
m.atr.int <- mlogit(Chosen ~ 0 + Price + brand + type , data=data.mlogit)
summary(m.atr.int)
##
## Call:
## mlogit(formula = Chosen ~ 0 + Price + brand + type, data = data.mlogit,
## method = "nr", print.level = 0)
##
## Frequencies of alternatives:
## pos 1 pos 2 pos 3
## 0.37429 0.32571 0.30000
##
## nr method
## 5 iterations, 0h:0m:0s
## g'(-H)^-1g = 6.86E-06
## successive function values within tolerance limits
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## Price -0.309299 0.071385 -4.3329 1.472e-05 ***
## brandGhirardelli 0.483377 0.220133 2.1958 0.028103 *
## brandGodiva 0.534987 0.205608 2.6020 0.009269 **
## brandHershey -0.453002 0.233326 -1.9415 0.052199 .
## brandLindt -0.150753 0.225934 -0.6672 0.504617
## typeDarkNuts -0.317797 0.208215 -1.5263 0.126937
## typeMilk 0.096331 0.215219 0.4476 0.654446
## typeMilkNuts -0.501818 0.219496 -2.2862 0.022241 *
## typeWhite -1.711444 0.261160 -6.5532 5.630e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log-Likelihood: -327.23
The results of the mlogit show the part worth estimates. The estimate is listed for each level along with the standard error. In this model, price is a continuous variable and the intercepts are not included. The estimates are interpreted relative to the base levels. For instance, our data suggests that Godiva is a significant predictor of whether a chocolate will be chosen, and all else remaining equal will be chosen more often than Dove. Likewise, white chocolate is also a significant predictor and all else remaining equal will be chosen less often than dark chocolate.
Sensitivity analysis allows us to estimate how market share would change if changes were make to the product, given our data and competitors. For example, if we wanted to explore making dark chocolate for the first time, what could we expect as an increase to market share.
For each level used in the experiment, this graphic shows how the base line product:
expand.grid(atr)[c(1),]
## brand type Price
## 1 Dove MilkNuts 0.5
would change given what the competitors are doing:
expand.grid(atr)[c(58,64,21,27,10),]
## brand type Price
## 58 Godiva Dark 0.7
## 64 Ghirardelli DarkNuts 0.7
## 21 Dove Milk 0.5
## 27 Lindt MilkNuts 0.6
## 10 Hershey Dark 0.5